The Queen said the day was filled with "sorrow and regret" as well as "pride".

Earlier, the monarch laid a wreath at a military cemetery in Bayeux.

'Helped end war'

The main ceremony took place on the French northern coast at Sword Beach, the code name for one of the Allies' five landing points where, following Mr Hollande's speech, scenes from the invasion were re-enacted.

The 1944 landings - involving 156,000 troops - were the first stage of the invasion of Nazi-occupied Europe.

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The Queen attended a ceremony at Bayeux cemetery along with other royals and French Prime Minister Manuel Valls

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Large screens at the Sword Beach ceremony showed veterans as part of the coverage

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The crowds were treated to a flypast by aircraft from World War Two, including Lancasters and Spitfires

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The Duke and Duchess of Cambridge attended a tea party in Arromanches, near Gold landing beach

By the end of D-Day on 6 June 1944, the Allies had established a foothold in France - an event that would eventually help bring the war to an end.

More than 4,000 British, American and Canadian troops lost their lives on that first day of the battle.

At the D-Day commemorations

Caroline Wyatt, BBC defence correspondent

The invasion of Arromanches, 70 years on, is almost over. For one brief sunny day, this small Normandy town has felt like the centre of the world. A world that has honoured, commemorated and celebrated the men whose unassuming courage shaped the Europe we live in today.

While world leaders met, talked and paid tribute just down the road, the square at Arromanches resembled a festival. But a festival in which the stars were in their 80s and 90s - and slightly bemused by all the fuss.

As veterans walked quietly on the beaches, some supported by walking sticks, others wordlessly given a helping arm by friends and families, they were clapped, cheered and thanked by those who'd come from across the continent to pay their respects.

It was an emotional week for one veteran we followed as he travelled to France. At the age of 90, Tony Colgan brought his grandson Anthony here, to Gold Beach - a place that defined his life.

"There was all hell breaking loose when we were about a mile off shore. You thought, 'this is your last day'.. and then suddenly, it all went silent, just for a matter of a minute or two," he remembers.

In Bayeux war cemetery, 200 of Tony Colgan's young Durham Light Infantry comrades lie buried, most in their late teens or early twenties. "They never even had a life," he says, unable to stop the tears.

Down the road in the village of Lingevres, Tony and his comrades lay a wreath in the place they liberated just a week or so after D-Day.

The local mayor promises them that their sacrifice is not forgotten. The children of the village whose future they assured lay wreaths every Remembrance Day, and on the 8th of May for Victory in Europe.

Media caption"I was a little bit surprised to see so many dead soldiers in the sea"

Speaking at the sun-drenched event, and in the face of high temperatures, Mr Hollande said: "It's up to us to have the same vision, the same courage, to be just as bright and have the same determination as those who came to these beaches 70 years ago."

The president also hailed "the courage of all these young men who came from all over the world to conquer - metre after metre, inch after inch - the beaches and the dunes".

"I really wish to pay tribute to the courage and the Germans who were actually victims of Nazi rule," he added.

"They were led into a war which was not theirs and which would have never been theirs. And today we really want to pay homage to all the victims of Nazi rule."

Mr Hollande also called for the beaches of Normandy to become a Unesco World Heritage site.

'Sheer courage'

A 21-gun salute and a flypast also formed part of proceedings at the Sword Beach ceremony, which was attended by UK Prime Minister David Cameron and German Chancellor Angela Merkel.

A Lancaster bomber, regarded as the workhorse of the RAF, flew over the crowds below, flanked by two Spitfires.

Media captionPresident Obama led a standing ovation, ahead of a 21-gun salute and fly-past at the Colleville-sur-Mer US cemetery

At Arromanches, near Gold landing beach where thousands of troops once came ashore, the crowds were led in prayer by Reverend Mandy Reynolds, the national chaplain of the Normandy Veterans Association.

And Prince William gave a speech in which he called D-Day a "great and terrible day".

"Great because it signalled the beginning of the end of Nazism. Terrible because so great a number of young men, and French men, women and children here and elsewhere in Normandy, lost their lives."

On Friday evening, speaking at a banquet at the Elysée Palace, the Queen said she and Prince Philip had been "stirred by the day's commemoration" and felt "sorrow and regret remembering the loss of many fine young soldiers, sailors and airmen".

But they also felt "pride at the sheer courage of the men who stormed those beaches, embodied in the veterans amongst us," she added.

"And... thankfulness, knowing that today, our nations are free and sovereign, because allied forces liberated this continent from occupation and tyranny."

'Thanks'

These events have drawn hundreds of thousands of people to the Normandy beaches, all outwardly here for the same reason but actually taking away very different things

Earlier in the day at Colleville-sur-Mer, US President Barack Obama said: "America's claim - our commitment to liberty, to equality, to freedom, to the inherent dignity of every human being - that claim is written in blood on these beaches, and it will endure for eternity."

Elsewhere, Prince Charles and the Duchess of Cornwall attended a Royal British Legion service at Bayeux Cathedral.

Following a morning service at the cathedral, many veterans left to walk to the nearby military cemetery where nearly 2,000 eventually gathered.

The BBC's Becky Kelly reported that crowds burst into applause as the veterans walk past, some people shouting "thanks".

In other events:

A flotilla of ships from the Allied nations led by HMS Bulwark sailed from Portsmouth to Normandy on Thursday

Prince Charles and the Duchess of Cornwall attended a remembrance ceremony at the Juno Beach Centre, Courseulles-sur-Mer, to commemorate Canada's role in the Normandy landings

Bernard Jordan, an 89-year-old D-Day veteran who went missing after apparently not telling care home staff that he was attending the anniversary commemorations, was found safe and well in Normandy. He left the home on Thursday morning wearing his war medals under a jacket and raincoat

By the end of D-Day, the Allies had established a foothold in France. Within 11 months Nazi Germany was defeated, as Soviet armies swept in from the east and captured Hitler's stronghold in Berlin.

Will you be marking the anniversary of D-Day? Were you involved in some way in the Normandy landings? Do you have family who were involved in the action, or the build up to that day? You can email haveyoursay@bbc.co.uk with your stories, using 'D-Day' in the subject.

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